Stochastic Landau-Lifshitz-Gilbert dynamical systems applied to spin glass models

The Edwards-Anderson model is a fundamental, well-studied spin glass Ising model that describes disordered magnetic materials with nearest neighbor interactions. In previous work, we demonstrated the ability of Landau-Lifshitz-Gilbert (LLG) dynamics to reach the ground state of the Sherrington-Kirkpatrick spin glass model with all-to-all connectivity across a range of system sizes [1]. This is achieved by transforming the Ising spins into macrospins that obey the LLG equation, subject to an uniaxial magnetic anisotropy that favors magnetic moments along the z-axis, and an annealing schedule. Here, we apply the same macrospin LLG dynamics method to the Edwards-Anderson model and investigate the average energy per spin as a function of system size as well as the spin glass susceptibility. To do so, we make use of a new GPU C++ implementation that can simulate very large system sizes at one-tenth or less of the time that was previously required.

1. Chen, Dairong and Kent, Andrew D. and Sels, Dries and Morone, Flaviano, Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems, Phys. Rev. Res. 7, 013129 (2025).